Coupled solitons in rare-earth doped two-mode fiber

doi:10.1364/OE.16.017441

Coupled solitons in rare-earth doped two-mode fiber

T. N. Dey, S. Dutta Gupta, and G. S. Agarwal »View Author Affiliations

Optics Express, Vol. 16, Issue 22, pp. 17441-17450 (2008)
http://dx.doi.org/10.1364/OE.16.017441

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Abstract

We present first ever analytical solutions for shape-preserving pulses in a Kerr nonlinear two-mode fiber doped with 3-level Λ atoms. The two modes are near-resonant with the two transitions of the atomic system. We show the existence of quasi-stable coupled bright-dark pairs if the group velocity dispersion has opposite signs at the two mode frequencies. We demonstrate the remarkable possibility allowed by the fiber dispersion for the existence of a new class of solutions for unequal coupling constants for the two modes. We present the conditions for existence and the analytical form of these solutions in presence of atomic detuning. We confirm numerically the analytical solutions for the spatio-temporal evolution of coupled solitary waves.

OCIS Codes
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(270.5530) Quantum optics : Pulse propagation and temporal solitons

ToC Category:
Nonlinear Optics

History
Original Manuscript: September 2, 2008
Revised Manuscript: October 13, 2008
Manuscript Accepted: October 13, 2008
Published: October 15, 2008

Citation
T. N. Dey, S. Dutta Gupta, and G. S. Agarwal, "Coupled solitons in rare-earth doped two-mode fiber," Opt. Express 16, 17441-17450 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-22-17441

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References

S. L. McCall and E. L. Hahn, "Self-induced transparency by pulsed coherent light," Phys. Rev. Lett. 18, 908-911 (1967) [CrossRef]
S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969). [CrossRef]
G. L. Lamb, Jr., "Analytical Descriptions of Ultrashort Optical Pulse Propagation in a Resonant Medium," Rev. Mod. Phys. 43, 99-124 (1971). [CrossRef]
H. A. Haus, "Physical interpretation of inverse scattering formalism applied to self-induced transparency," Rev. Mod. Phys. 51, 331-339 (1971). [CrossRef]
A. I. Maimistov, A. M. Bhasrov, S. O. Elyutin, and M. Y. Sklyarov, "Present state of self-induced transparency theory," Phys. Rep. 191, 1-108 (1990). [CrossRef]
R. Grobe, F. T. Hioe, and J. H. Eberly, "Formation of Shape-Preserving Pulses in a Nonlinear Adiabatically Integrable System," Phys. Rev. Lett. 73, 3183-3186 (1994). [CrossRef] [PubMed]
J. H. Eberly, "Transmission of dressed fields in three-level media," Quantum Semiclassic. Opt. 7, 373-384 (1995). [CrossRef]
A. Rahman and J. H. Eberly, "Theory of shape-preserving short pulses in inhomogeneously broadened three-leve media," Phys. Rev. A 58, R805-R808 (1998). [CrossRef]
J. H. Eberly and V. V. Kozlov, " Wave Equation for Dark Coherence in Three-Level Media," Phys. Rev. Lett. 88, 243604-1-243604-4 (2002). [CrossRef]
G. Vemuri, G. S. Agarwal, and K. V. Vasavada, "Cloning, Dragging, and Parametric Amplification of Solitons in a Coherently Driven, Nonabsorbing System," Phys. Rev. Lett. 79, 3889-3892 (1997). [CrossRef]
D. P. Caetano, S. B. Cavalcanti, and J. M. Hickmann, "Coherent interaction effects in pulses propagating through a doped nonlinear dispersive medium," Phys. Rev. E 65, 036617-1-036617-6 (2002). [CrossRef]
S. E. Harris, J. E. Field, and A. Kasapi, "Dispersive properties of electromagnetically induced transparency," Phys. Rev. A 46, R29-R32 (1992). [CrossRef] [PubMed]
L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas," Nature, 397, 594-598 (1999). [CrossRef]
G. P. Agarwal, Nonlinear Fiber Optics 2nd Ed., (Academic Press, San Diego CA 1995).
S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, "Optical solitary waves induced by cross-phase modulation," Opt. Lett. 13, 871-873 (1988). [CrossRef] [PubMed]
Q. Yang, J. T. Seo, B. Tabibi, and H. Wang, "Slow Light and Superluminality in Kerr Media without a Pump," Phys. Rev. Lett. 95, 063902-1-063902-4 (2005). [CrossRef]
M. Nakazawa, E. Yamada, and H. Kubota, "Coexistence of self-induced transparency soliton and nonlinear Schrdinger soliton," Phys. Rev. Lett. 66, 2625-2628 (1991). [CrossRef] [PubMed]
M. Nakazawa, E. Yamada, and H. Kubota, "Coexistence of a self-induced-transparency soliton and a nonlinear Schrdinger soliton in an erbium-doped fiber," Phys. Rev. A 44, 5973-5987 (1991). [CrossRef] [PubMed]
M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, "Self-induced-transparency solitons in an erbium-doped fiber waveguide," Phys. Rev. A 45, R23-R26 (1992). [CrossRef] [PubMed]
S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, "Resonant Optical Interactions with Molecules Confined in Photonic Band-Gap Fibers," Phys. Rev. Lett. 94, 093902-1-093902-4 (2005). [CrossRef]
S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-Light-Level Optical Interactions with Rubidium Vapor in a Photonic Band-Gap Fiber," Phys. Rev. Lett. 97, 023603-1-023603-4 (2006). [CrossRef]

Agarwal, G. S.
Behroozi, C. H.
Bhasrov, A. M.
Dutton, Z.
Eberly, J. H.
Elyutin, S. O.
Field, J. E.
Grobe, R.
Hahn, E. L.
Harris, S. E.
Hau, L. V.
Haus, H. A.
Hioe, F. T.
Kasapi, A.
Kimura, Y.
Kubota, H.
Kurokawa, K.
Lamb, G. L.
Maimistov, A. I.
McCall, S. L.
Nakazawa, M.
Rahman, A.
Sklyarov, M. Y.
Stegeman, G. I.
Suzuki, K.
Trillo, S.
Vasavada, K. V.
Vemuri, G.
Wabnitz, S.
Wright, E. M.
Yamada, E.

Nature

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas," Nature, 397, 594-598 (1999). [CrossRef]

Opt. Lett.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, "Optical solitary waves induced by cross-phase modulation," Opt. Lett. 13, 871-873 (1988). [CrossRef] [PubMed]

Phys. Rep.

A. I. Maimistov, A. M. Bhasrov, S. O. Elyutin, and M. Y. Sklyarov, "Present state of self-induced transparency theory," Phys. Rep. 191, 1-108 (1990). [CrossRef]

Phys. Rev.

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969). [CrossRef]

Phys. Rev. A

A. Rahman and J. H. Eberly, "Theory of shape-preserving short pulses in inhomogeneously broadened three-leve media," Phys. Rev. A 58, R805-R808 (1998). [CrossRef]
S. E. Harris, J. E. Field, and A. Kasapi, "Dispersive properties of electromagnetically induced transparency," Phys. Rev. A 46, R29-R32 (1992). [CrossRef] [PubMed]
M. Nakazawa, E. Yamada, and H. Kubota, "Coexistence of a self-induced-transparency soliton and a nonlinear Schrdinger soliton in an erbium-doped fiber," Phys. Rev. A 44, 5973-5987 (1991). [CrossRef] [PubMed]
M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, "Self-induced-transparency solitons in an erbium-doped fiber waveguide," Phys. Rev. A 45, R23-R26 (1992). [CrossRef] [PubMed]

Phys. Rev. Lett.

S. L. McCall and E. L. Hahn, "Self-induced transparency by pulsed coherent light," Phys. Rev. Lett. 18, 908-911 (1967) [CrossRef]
G. Vemuri, G. S. Agarwal, and K. V. Vasavada, "Cloning, Dragging, and Parametric Amplification of Solitons in a Coherently Driven, Nonabsorbing System," Phys. Rev. Lett. 79, 3889-3892 (1997). [CrossRef]
R. Grobe, F. T. Hioe, and J. H. Eberly, "Formation of Shape-Preserving Pulses in a Nonlinear Adiabatically Integrable System," Phys. Rev. Lett. 73, 3183-3186 (1994). [CrossRef] [PubMed]
M. Nakazawa, E. Yamada, and H. Kubota, "Coexistence of self-induced transparency soliton and nonlinear Schrdinger soliton," Phys. Rev. Lett. 66, 2625-2628 (1991). [CrossRef] [PubMed]

Quantum Semiclassic. Opt.

J. H. Eberly, "Transmission of dressed fields in three-level media," Quantum Semiclassic. Opt. 7, 373-384 (1995). [CrossRef]

Rev. Mod. Phys.

G. L. Lamb, Jr., "Analytical Descriptions of Ultrashort Optical Pulse Propagation in a Resonant Medium," Rev. Mod. Phys. 43, 99-124 (1971). [CrossRef]
H. A. Haus, "Physical interpretation of inverse scattering formalism applied to self-induced transparency," Rev. Mod. Phys. 51, 331-339 (1971). [CrossRef]

Other

D. P. Caetano, S. B. Cavalcanti, and J. M. Hickmann, "Coherent interaction effects in pulses propagating through a doped nonlinear dispersive medium," Phys. Rev. E 65, 036617-1-036617-6 (2002). [CrossRef]
J. H. Eberly and V. V. Kozlov, " Wave Equation for Dark Coherence in Three-Level Media," Phys. Rev. Lett. 88, 243604-1-243604-4 (2002). [CrossRef]
G. P. Agarwal, Nonlinear Fiber Optics 2nd Ed., (Academic Press, San Diego CA 1995).
S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, "Resonant Optical Interactions with Molecules Confined in Photonic Band-Gap Fibers," Phys. Rev. Lett. 94, 093902-1-093902-4 (2005). [CrossRef]
S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-Light-Level Optical Interactions with Rubidium Vapor in a Photonic Band-Gap Fiber," Phys. Rev. Lett. 97, 023603-1-023603-4 (2006). [CrossRef]
Q. Yang, J. T. Seo, B. Tabibi, and H. Wang, "Slow Light and Superluminality in Kerr Media without a Pump," Phys. Rev. Lett. 95, 063902-1-063902-4 (2005). [CrossRef]

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